Problems $(15$ pts each$)$

Table $1-1$ below provides annual peak stream flows and corresponding years for Wolf Creek via USGS gage $02378170.$ The standard deviation of these data is $2,134,$ while the skew is known to be $2\mathrm{.}11$; however, it has been determined that the data follow a normal distribution. Using Table $1-2,$ determine$/$answer the following: $40\%,20\%,10\%$

S

a$.$ The $0\mathrm{.}04,0\mathrm{.}02,$ and $0\mathrm{.}01$ AEP flows. $52\mathrm{.}2,26\mathrm{.}1,13\mathrm{.}1$

s

b$.$ The probability of observing a $6,000cfs$ event. $30\%$

$$

c$.$ The probability of observing the $100-$year event in a $15-$year period. $20\%$

Bonus $(3$ pts$)$: What term is used to define abnormal peak flows observed in the years $2014$ and $2020?$

Table $1-1$: Peak Streamflow Data at USGS $02378170$

$\backslash$table$[[$Water Year,Flow $($cfs$),$Water Year,Flow $($cfs$)],[2009,974,2016,409],[2010,792,2017,1,080],[2011,620,2018,783],[2012,461,2019,1,020],[2013,898,2020,5,770],[2014,7,040,2021,1,860],[2015,478,-,-]]$

Table $1-2$: Percentiles of the Normal Distribution

$\backslash$table$[[F(z),z,F(z),z$